(1) Field of the Invention
The present invention relates to a method for multiple criteria decision making (MCDM). More particularly, the invention relates to an MCDM method that is suitable for maintaining a complex article that comprises multiple components.
(2) Description of the Art
There are many situations that require the best solution to be found to a multi-objective, often termed multi-criteria, problem. Examples range from financial and resource planning problems to complex technical maintenance problems. The various criteria are often conflicting and solutions that provide an acceptable trade-off are sought.
A variety of techniques are known for finding solutions to complex multi-criteria problems. One known approach is to combine the various objectives, possibly applying different weightings to different criteria, to form an aggregate problem. An optimisation process can then be applied to find the best solutions to the aggregate problem. Techniques of this type are often termed Multiple Attribute Value Theory or Multiple Attribute Utility Theory (MAVT/MAUT) and are described in more detail by R. Keeny and H. Raiffa in the book “Decisions with Multiple Objectives”, Wiley, 1976. However, approaches of this type place a high reliance on the particular weightings that are used when combining the criteria and failure to meet certain criteria can be masked by meeting a number of the other criteria very well.
True multi-criteria optimisation techniques are also known in which each criterion is considered separately. In such techniques, optimal solutions are sought that respect all the separate criteria. The ideal solution to such multi-criteria problems is the so-called Pareto optimal set; this is a set of solutions each of which are not dominated by the others in terms of all the criteria. Evolutionary algorithms (EAs), which include genetic algorithms (GAs), are examples of well known techniques that are particularly suited for true multi-criteria optimisation.
Existing MCDM techniques of the type described above are inherently incapable of solving problems in which the various criteria have an associated uncertainty. To account for any uncertainty in the criteria, it is necessary to form a so-called decision tree that provides a hierarchical depiction of decisions at different levels. Typically, such decision trees are formed using bounding scenarios for future events; for example the best and worst possible scenarios could be considered. Known MCDM techniques of the type described above can then be applied to the various branches of the decision tree to produce scores for each possible consequence. Although the formation of a decision tree can deal with some degree of uncertainty, such a technique can be seen to be extremely complex when there are multiple criteria having high levels of uncertainty.
A number of techniques are known for describing criteria using probabilistic values. For example, it is possible to use Bayesian belief networks (BBNs) as described in “Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference”, by J. Pearl, Morgan Kauffman, San Mateo, Calif. 1988. However, a skilled person would appreciate that the probabilistic values generated for each criteria would have to be converted to single values before any of the known MCDM evaluation techniques described above could be applied thereto. Conversion of the probabilistic criteria to singular values would thus remove any advantage associated with describing criteria probabilistically using a BBN.
An example of a complex technical problem in which criteria can be described using probabilistic values is the problem of ensuring that a complex piece of machinery, such as a train, aircraft or complex micro-electronic device, is maintained so as to continually meet certain technical specifications (e.g. performance or safety criteria) throughout its lifetime. In particular, such a problem may involve assessing potential options for dealing with components that become obsolete during the complex article's lifetime. In such an example, there may be many potential options for dealing with each obsolete component and it is thus an extremely complex task to find and implement the suite of component replacement options that provide the best trade-off against the necessary criteria at a system, rather than component, level.